Parallel multigrid method for solving elliptic equations

On Development of Parallel Algorithms for Solving Parabolic and Elliptic Equations

“…We consider only the classical version of the multigrid method with resampling on all additional grid levels. Numerous meaningful examples of solving problems with various degrees of complexity (with discontinuous anisotropic coefficients and significant anisotropy) are given in [18][19][20][21]. For demonstration of the computational efficiency, we provide the results of the solution of the simplest equation u t = Δu + f in the parallelepiped…”

“…The amplitude of such components decreases almost inversely proportional to the frequency, which corresponds to the needs of the multigrid method. As a result, for the geometric classical multigrid method (MM) on Cartesian grids, we have constructed an effective parallel adaptive implementation (see [18][19][20][21]); now we develop it for the algebraic multigrid method.…”

The technology of large-scale CFD simulations

“…First, it is the growth in productivity and the improvement in supercomputer architectures aimed at enhancing energy efficiency and reducing the cost of capacity utilization. Second, it is the development of numerical methods, models, and algorithms bringing down the computational cost of the calculations and making possible the simulation of turbulence and reduction in the requirements for spatial resolution [1,2]; improvement in parallel SLAE solvers, in particular, methods based on Krylov subspaces [3], and multigrid methods [4,5]; cost-effective schemes of high-order spatial approximations such as schemes with the quasione-dimensional (1D) reconstruction [6,7]; and cheaper time integration, e.g., through the use of schemes with a local or fractional step.…”

Application of the Method of Pyramid for Synthesis of Parallel Algorithm for Difference Solution of the Twodimensional Partial Differentials Equation

“…The specified circumstance induces researchers to development of vector and parallel methods of solution of systems of linear equations of a tape look [5,6,7,8], for the purpose of decrease in duration of model operation. In recent work [9] the parallel algorithm of a multigrid method of solution of elliptical equations by means of Chebyshev iterative procedure is offered. Authors hold its testing on a supercomputer "Lomonosov", trying to obtain on 64 computing clusters (everyone contains 2 six nuclear Intel Xeon X5670 processors) acceleration of calculations by 25 times in comparison with method of prime iteration.…”